## VINCIA QCD Antenna Shower Settings

Here, parameters specific to VINCIA's QCD antenna shower are collected. See the main VINCIA antenna shower page for more general parameters that are common to both the QCD and QED showers.

### Main Switches

`flag` Vincia:doII (`default = on`)
Main switch for initial-initial (II) antennae on/off (subject to the `PartonLevel` settings).

`flag` Vincia:doIF (`default = on`)
Main switch for initial-final (IF) antennae on/off (subject to the `PartonLevel` settings). Note: setting this to off will switch off both the initial- and final-state ends of corresponding QCD antennae.

`flag` Vincia:doFF (`default = on`)
Main switch for final-final (FF) antennae on/off (subject to choices made at `PartonLevel`).

`flag` Vincia:doRF (`default = on`)
Main switch for resonance-final (RF) antennae on/off (subject to the `PartonLevel` settings). Note: setting this to off will switch off both the resonance- and final-state ends of corresponding QCD antennae.

`mode` Vincia:nGluonToQuark (`default = 5`; `minimum = 0`; `maximum = 6`)
Number of allowed quark flavours in final-state gluon splittings, g → q qbar, during the shower evolution, phase space permitting. E.g., a change to 4 would exclude g → b bbar but would include the lighter quarks, etc. Note that this parameter does not directly affect the running coupling.

`flag` Vincia:convertGluonToQuark (`default = on`)
Allow incoming gluons to backwards-evolve into (anti)quarks during the initial-state shower evolution.

`flag` Vincia:convertQuarkToGluon (`default = on`)
Allow incoming (anti)quarks to backwards-evolve into (anti)quarks during the initial-state shower evolution.

### The QCD coupling in the Vincia Shower

The strong coupling constant is specified by providing its reference value (interpreted as given at the Z pole in the MSbar scheme) and running properties (loop order, behaviour at top threshold, and any low-scale regularisation/dampening).

Note that VINCIA only uses one global value for the definition of the strong coupling constant. The effective couplings used in shower branchings (renormalisation scheme and scale) are governed by separate parameters which are specified under initial- and final-state showers respectively.

VINCIA implements its own instance of PYTHIA's `AlphaStrong` class for the strong coupling. You can find more documentation of the class in the section on Standard-Model Parameters in the PYTHIA documentation. Here, we list the specific parameters and switches governing its use in VINCIA.

The free parameter of the strong coupling constant is specified by

`parm` Vincia:alphaSvalue (`default = 0.118`; `minimum = 0.06`; `maximum = 2.0`)
The value of αs at the scale mZ, in the MSbar scheme. The default value is chosen to be in agreement with the current world average. The effective value used for showers may be further affected by translation to the CMW scheme (below) and by renormalisation-scale prefactors given for FSR and ISR showers separately.

`mode` Vincia:alphaSorder (`default = 2`; `minimum = 0`; `maximum = 2`)
Order at which αs runs,
`option` 0 : zeroth order, i.e. αs is kept fixed.
`option` 1 : first order, i.e., one-loop running.
`option` 2 : second order, i.e., two-loop running.

Resummation arguments [Cat91] indicate that a set of universal QCD corrections can be absorbed in coherent parton showers by applying the so-called CMW rescaling of the MSbar value of Lambda_QCD, defined by

αs(CMW) = αs(MSbar) * (1 + K * αs(MSbar) / 2π)
with K = CA * (67/18 - π2/6) - 5/9nf. The translation amounts to an NF-dependent rescaling of Lambda_QCD, relative to its MSbar value, by a factor 1.661 for NF=3, 1.618 for NF=4, 1.569 for NF=5, and 1.513 for NF=6. Although the original argument strictly concerned only the eikonal for soft-gluon emissions, the current version of VINCIA only offers the option of switching the rescaling of Lambda_QCD on or off. When on, the rescaling is applied to all branching types, not just gluon emissions.

`flag` Vincia:useCMW (`default = on`)
If set to on, the alphaS value used for shower branchings will be translated from the MSbar value to the CMW ("MC") scheme. If set to off, the MSbar value will be used.

Note 1: If using VINCIA with an externally defined matching scheme, be aware that the CMW rescaling may need be taken into account in the context of matrix-element matching. Note also that this option has only been made available for timelike and spacelike showers, not for hard processes.
Note 2: Tunes using this option need roughly 10% lower values of alphas(mZ) than tunes that do not.

For both one- and two-loop running, the `AlphaStrong` class automatically switches from 3-, to 4-, and then to 5-flavour running as one passes the s, c, and b thresholds, respectively, with matching equations imposed at each flavour treshold to ensure continuous values. By default, a change to 6-flavour running is also included above the t threshold, though this can be disabled using the following parameter:

`mode` Vincia:alphaSnfmax (`default = 6`; `minimum = 5`; `maximum = 6`)
`option` 5 : Use 5-flavour running for all scales above the b flavour threshold (old default).
`option` 6 : Use 6-flavour running above the t threshold (new default).

`parm` Vincia:alphaSmuFreeze (`default = 0.75`; `minimum = 0.0`; `maximum = 10.0`)
The behaviour of the running coupling in the far infrared is regulated by a shift in the effective renormalisation scale, to μeff 2 = μfreeze2 + μR2.

`parm` Vincia:alphaSmax (`default = 2.0`; `minimum = 0.1`; `maximum = 10.0`)
Largest allowed numerical value for alphaS. I.e., the running is forced to plateau at this value.

#### Choice of Renormalisation Scales for Shower Branchings

When `Vincia:alphaSorder` is non-zero, the actual value of alphaS used for shower branchings is governed by the choice of scheme (MSbar or CMW, see the section on AlphaStrong and then by running to the scale kR*Q2, at which the shower evaluates αs, with Q2 the Vincia evolution scale of the branching. The multiplicative scale factor kR is given by

`parm` Vincia:renormMultFacEmitF (`default = 0.66`; `minimum = 0.1`; `maximum = 10.0`)
for gluon emission

and

`parm` Vincia:renormMultFacSplitF (`default = 0.8`; `minimum = 0.1`; `maximum = 10.0`)
for gluon splitting.

For initial-state branchings, the functional form of muR is given by the evolution variable and the scale factor kR is given by

`parm` Vincia:renormMultFacEmitI (`default = 0.66`; `minimum = 0.1`; `maximum = 10.0`)
for gluon emission,

`parm` Vincia:renormMultFacSplitI (`default = 0.5`; `minimum = 0.1`; `maximum = 10.0`)
for gluon splitting (quark in the initial state backwards evolving into a gluon),

`parm` Vincia:renormMultFacConvI (`default = 0.5`; `minimum = 0.1`; `maximum = 10.0`)
for gluon conversion (gluon in the initial state backwards evolving into a (anti)quark)

### Colour Charges

The normalisation of colour factors in VINCIA is chosen such that the coupling factor for all antenna functions is αS/4π. With this normalisation, all gluon-emission colour factors tend to NC in the large-NC limit while all gluon-splitting colour factors tend to unity. (Thus, e.g., the default normalisation of the qqbar → qgqbar antenna function is 2CF.)

`parm` Vincia:QQemitII:chargeFactor (`default = 2.66666667`)
Emission of a final-state gluon from an initial-state qqbar pair.

`parm` Vincia:GQemitII:chargeFactor (`default = 2.83333333`)
Emission of a final-state gluon from an initial-state qg (or gqbar) pair.

`parm` Vincia:GGemitII:chargeFactor (`default = 3.0`)
Emission of a final-state gluon from an initial-state gg pair.

`parm` Vincia:QXSplitII:chargeFactor (`default = 1.0`)
Quark in the initial state backwards evolving into a gluon and emitting an antiquark in the final state

`parm` Vincia:GXConvII:chargeFactor (`default = 2.66666667`)
Gluon in the initial state backwards evolving into a quark and emitting a quark in the final state (gluon conversion)

`parm` Vincia:QQemitIF:chargeFactor (`default = 2.66666667`)
Gluon emission of an initial-final qq pair

`parm` Vincia:GQemitIF:chargeFactor (`default = 2.83333333`)
Gluon emission off an initial-final gq pair

`parm` Vincia:QGemitIF:chargeFactor (`default = 2.83333333`)
Gluon emission of an initial-final qg pair

`parm` Vincia:GGemitIF:chargeFactor (`default = 3.0`)
Gluon emission of an initial-final gg pair

`parm` Vincia:QXSplitIF:chargeFactor (`default = 1.0`)
Quark in the initial state evolving backwards into a gluon and emitting an antiquark in the final state

`parm` Vincia:GXConvIF:chargeFactor (`default = 2.66666667`)
Gluon in the initial state backwards evolving into a quark and emitting a quark into the final state (gluon conversion)

`parm` Vincia:XGSplitIF:chargeFactor (`default = 1.0`)
Gluon splitting in the final state

`parm` Vincia:QQEmitFF:chargeFactor (`default = 2.66666667`)

`parm` Vincia:QGEmitFF:chargeFactor (`default = 2.85`)

`parm` Vincia:GGEmitFF:chargeFactor (`default = 3.0`)

`parm` Vincia:QGSplitFF:chargeFactor (`default = 1.0`)

`parm` Vincia:GGSplitFF:chargeFactor (`default = 1.0`)

`parm` Vincia:GXSplitFF:chargeFactor (`default = 1.0`)

`parm` Vincia:QQEmitRF:chargeFactor (`default = 2.66666667`)

`parm` Vincia:QGEmitRF:chargeFactor (`default = 2.85`)

`parm` Vincia:XGSplitRF:chargeFactor (`default = 1.0`)
Note: the two permutations g-g → g-q+qbar and g-g → qbar+q-g are explicitly summed over in the code (with appropriate swapping of invariants in the latter case).

### Kinematics and Recoils

While the CM momenta of a 2→3 branching are fixed by the generated invariants (and hence by the antenna function), the global orientation of the produced 3-parton system with respect to the rest of the event (or, equivalently, with respect to the original dipole-antenna axis) suffers from an ambiguity outside the LL limits, which can be significant in regions where the leading logs are suppressed or absent.

To illustrate this ambiguity, consider the emissision of a gluon from a qqbar antenna with some finite amount of transverse momentum (meaning transverse to the original dipole-antenna axis, in the CM of the dipole-antenna). The transverse momenta of the qqbar pair after the branching must now add up to an equal, opposite amount, so that total momentum is conserved, i.e., the emission generates a recoil. By an overall rotation of the post-branching 3-parton system, it is possible to align either the q or the qbar with the original axis, such that it becomes the other one that absorbs the entire recoil (the default in showers based on 1→2 branchings such as old-fashioned parton showers and Catani-Seymour showers), or to align both of them slightly off-axis, so that they share the recoil (the default in VINCIA, see illustration below).

#### Kinematics and Recoils for II Antennae

The post-branching momenta are fixed by the following requirements:
1) The direction of the initial state partons is aligned with the beam axis (z-axis).
2) The invariant mass and the rapidity of the final state recoiler are not changed by the branching. This allows a direct construction of the post-branching momenta in the lab frame.

#### Kinematics and Recoils for IF Antennae

For IF branchings, Vincia contains implementations of two different kinematics maps, called "local" and "global" in what follows.

In the "local map", the initial-state parton recoils longitudinally, and there is no recoil imparted to any partons that do not participate directly in the branching. (I.e., recoil effects are absorbed locally within the branching antenna, and no partons outside of it are affected.) This is equivalent to saying that any transverse momentum associated with the emitted parton (j) is absorbed by the other final-state parton (k). This allows a simple construction of the post-branching momenta in the centre-of-mass frame of the initial-final antenna.

The "global map" allows for an overall transverse recoil associated with the initial-state leg to be imparted to the system of final-state partons other than those participating directly in the branchings. This is equivalent to saying that any transverse momentum associated with the emitted parton (j) is absorbed by the initial-stage leg (a), after which a Lorentz transformation brings it (plus the final-state system) back to having beam-collinear kinematics. The recoil vanishes For final-state collinear kinematicsbut is in general nonzero outside that limit.

Intuitively, the local map should be appropriate for final-state splittings, while the global one would be appropriate for initial-state ones. The full story is more complicated, partly since soft wide-angle radiation intrinsically represents interference between the two cases, and partly because the phase-space limits for the two maps (outside of the strict soft and collinear limits) are different. (The x < 1 constraint translates to slightly different constraints on the branching invariants for the two maps, as does positivity of the Gram determinant.) A probabilistic selection is therefore made between the local and global maps, using a form obtained by R. Verheyen based on comparisons to DIS matrix elements, P(global) = (sAK - saj)^2/[ (sAK + sjk)^2 + (sAK - saj)^2 ] * Theta( sAK - saj ), with Theta the unit step function (since the momenta in the global map always become unphysical for saj > sAK).

`mode` Vincia:kineMapIF (`default = 1`; `minimum = 1`; `maximum = 3`)
`option` 1 : Local recoil map.
`option` 2 : Gluon emissions use a probabilistic selection between the global and local maps. Antennae that only contain initial-state singularities always use the global one. Antennae that only contain final-state singularities always use the local one.
`option` 3 : Probabilistic selection between the global and and local maps, for all IF branchings irrespective of their singularity structure.

When using the probabilistic selection, it is possible (in phase-space regions well away from the strict soft and collinear limits) that the selected kinematics map produces unphysical momenta (with x > 1 or negative energies) for the given branching invariants, while the other map would give physical momenta. In such cases, one has to choose whether the given phase-space point should be vetoed, or whether the other map should be allowed to be used instead to construct the kinematics.

`flag` Vincia:kineMapIFretry (`default = off`)
`option` off : If the map selected according to the probabilistic choice above returns unphysical momenta, the trial branching is vetoed.
`option` on : If the map selected according to the probabilistic choice above returns unphysical momenta, the other map is tried. Only if both maps fail to produce physical momenta is the trial branching vetoed.

#### Kinematics and Recoils for FF Antennae

`mode` Vincia:kineMapFFemit (`default = 3`; `minimum = 1`; `maximum = 3`)
Selects which method to use for choosing the Euler angle for the global orientation of the post-branching kinematics construction for gluon emissions.
`option` 1 : The ARIADNE angle (see illustration). The recoiling mothers share the recoil in proportion to their energy fractions in the CM of the dipole-antenna. Tree-level expansions of the VINCIA shower compared to tree-level matrix elements through third order in alphaS have shown this strategy to give the best overall approximation, followed closely by the KOSOWER map below.
`option` 2 : LONGITUDINAL. The parton which has the smallest invariant mass together with the radiated parton is taken to be the "radiator". The remaining parton is taken to be the "recoiler". The recoiler remains oriented along the dipole axis in the branching rest frame and recoils longitudinally against the radiator + radiated partons which have equal and opposite transverse momenta (transverse to the original dipole-antenna axis in the dipole-antenna CM). Comparisons to higher-order QCD matrix elements show this to be by far the worst option of the ones so far implemented, hence it could be useful as an extreme case for uncertainty estimates, but should probably not be considered for central tunes. (Note: exploratory attempts at improving the behaviour of this map, e.g., by selecting probabilistically between the radiator and the recoiler according to approximate collinear splitting kernels, only resulted in marginal improvements. Since such variations would introduce additional complications in the VINCIA matching formalism, they have not been retained in the distributed version.)
`option` 3 : The KOSOWER map. Comparisons to higher-order QCD matrix elements show only very small differences between this and the ARIADNE map above, but since the KOSOWER map is sometimes used in fixed-order contexts, we deem it interesting to include it as a complementary possibility. (Note: the KOSOWER maps in fact represent a whole family of kinematics maps. For experts, the specific choice made here corresponds to using r=sij/(sij+sjk) in the definition of the map.)

`mode` Vincia:kineMapFFsplit (`default = 2`; `minimum = 0`; `maximum = 3`)
Selects which method to use for choosing the Euler angle for the global orientation of the post-branching kinematics construction for gluon splittings.
`option` 1 : The ARIADNE angle (see illustration). The recoiling mothers share the recoil in proportion to their energy fractions in the CM of the dipole-antenna. Tree-level expansions of the VINCIA shower compared to tree-level matrix elements through third order in alphaS have shown this strategy to give the best overall approximation, followed closely by the KOSOWER map below.
`option` 2 : LONGITUDINAL. For gluon splittings, this choice forces the recoiler to always recoil purely longitudinally (in the antenna CM) regardless of the size of the branching invariants.
`option` 3 : The KOSOWER map. Comparisons to higher-order QCD matrix elements show only very small differences between this and the ARIADNE map above, but since the KOSOWER map is sometimes used in fixed-order contexts, we deem it interesting to include it as a complementary possibility. (Note: the KOSOWER maps in fact represent a whole family of kinematics maps. For experts, the specific choice made here corresponds to using r=sij/(sij+sjk) in the definition of the map.)

#### Kinematics and Recoils for RF Antennae

`mode` Vincia:kineMapRFemit (`default = 1`; `minimum = 1`; `maximum = 2`)
There is only one choice of kinematics map for resonance emissions. However there is a freedom to choose the recoiler(s).
`option` 1 : Takes all non-colour-connected daughters in the resonance decay system as the recoilers.
`option` 2 : Takes the original non-colour-connected daughter of the resonance to always take the full recoil. E.g. in t->bW the recoiler is always the W. This is equivalent to setting TimeShower:recoilToColoured = off for Pythia.

`mode` Vincia:kineMapRFsplit (`default = 1`; `minimum = 1`; `maximum = 2`)
Same as above, but for R-g splittings.
`option` 1 : Takes all non-colour-connected daughters in the resonance decay system as the recoilers.
`option` 2 : Takes the original non-colour-connected daughter of the resonance to always take the full recoil. E.g. in t->bW the recoiler is always the W. This is equivalent to setting TimeShower:recoilToColoured = off for Pythia.

### Lower Cutoffs for the QCD evolution

The hadronisation cutoff, a.k.a. the infrared regularisation scale, defines the resolution scale at which the perturbative shower evolution is stopped. Thus, perturbative emissions below this scale are treated as fundmanentally unresolvable and are in effect inclusively summed over.

Important Note: when hadronisation is switched on, there is a delicate interplay between the hadronisation scale used in the shower and the parameters of the hadronisation model. Ideally, the parameters of the hadronisation model should scale as a function of the shower cutoff. This scaling does not happen automatically in current hadronisation models, such as the string model employed by PYTHIA. Instead, the parameters of the hadronisation model are tuned for one specific shower setting at a time and should be retuned if changes are made to the shower cutoff.

`parm` Vincia:cutoffScaleFF (`default = 0.75`; `minimum = 0.1`; `maximum = 10.0`)
This parameter sets the value (in GeV) of the final state shower cutoff. For `evolutionType = 1` it is interpreted as a cutoff on ARIADNE pT, while for `evolutionType = 2` it is interpreted as a cutoff on invariant mass.

`parm` Vincia:cutoffScaleII (`default = 1.6`; `minimum = 0.1`; `maximum = 10.0`)
This parameter sets the value (in GeV) of the shower cutoff for initial-initial antennae.

`parm` Vincia:cutoffScaleIF (`default = 1.6`; `minimum = 0.1`; `maximum = 10.0`)
This parameter sets the value (in GeV) of the shower cutoff for initial-final antennae.

`parm` Vincia:ThresholdMB (`default = 4.8`)
threshold (mass, in GeV) for bottom quark production.

`parm` Vincia:ThresholdMC (`default = 1.5`)
threshold (mass, in GeV) for charm quark production.

### Other QCD Settings

#### Subleading Colour

During the perturbative shower evolution, the first aspect of subleading colour is simply what colour factors are used for the antenna functions. In a strict leading-colour limit, one would use CA for all antennae, thus overestimating the amount of radiation from quarks (note that we use a normalisation convention in which the colour factor for quarks is 2CF, hence the difference is explicitly subleading in colour). A more realistic starting point is to use 2CF for quark-antiquark antennae, CA for gluon-gluon ones, and something inbetween for quark-gluon ones. The following switch determines whether and how subleading-colour corrections are treated in the evolution:

`mode` Vincia:modeSLC (`default = 2`; `minimum = 0`; `maximum = 3`)
`option` 0 : Strict LC evolution. All gluon-emission colour factors are forced equal to CA thus overcounting the radiation from quarks. Note that matrix-element corrections will still generate corrections to the evolution up to the matched number of legs.
`option` 1 : Simple Colour Factors. The `chargeFactor` parameters for each of the antenna functions are used to set the colour factor for each type of gluon-emission antenna; see the section on antenna functions. (Typically, 2CF for qqbar antennae, CA for gg antennae, and the average of 2CF and CA for qg antennae.)
`option` 2 : Interpolating Colour Factors. The colour factor for quark-antiquark antennae is forced equal to 2CF. Gluon-gluon antennae are normalised to CA. The colour factor for QG antennae is 2CF * (1-yij)/(2-yij-yjk) + CA * (1-yjk)/(2-yij-yjk), which is just a simple interpolation between CA in the gluon-collinear limit and 2CF in the quark-collinear limit. More sophisticated choices could also be motivated and may be interesting to explore in future versions.
`option` 3 : Only used for development purposes.

Colour flow is traced using Les-Houches style colour tags, augmented by letting the last digit encode the "colour index", running from 1 to 9, described further in the section below on antenna swing. One ambiguity arises in gluon emission as to which of the daughter antennae should inherit the "parent" colour tag/index, and which should be assigned a new one. This is controlled by the following parameter:

`mode` Vincia:CRinheritMode (`default = 1`; `minimum = -2`; `maximum = 2`)
`option` 0 : Random
`option` 1 : The daughter with the largest invariant mass has a probability 1/(1 + r) to inherit the parent tag, with r < 1 the ratio of the smallest to the largest daughter invariant masses squared.
`option` 2 : The daughter with the largest invariant mass always inherits the parent tag (winner-takes-all extreme variant of option 1).
`option` -1 : (Unphysical, intended for theory-level studies only). Inverted variant of option 1, so that the daughter with the smallest invariant mass preferentially inherits the parent colour tag.
`option` -2 : (Unphysical, intended for theory-level studies only). Inverted variant of option 2, so that the daughter with the smallest invariant mas always inherits the parent colour tag.